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<span class="kw">let </span><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a></span>)</span><br/>  for <font color="Olive" title="b2">k</font>, <font color="Olive" title="b3">m</font>, <font color="Olive" title="b4">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="flang_2.html#K1" title="FLANG_2:func.1">|^</a> (<font color="Olive" title="b3">m</font>,<font color="Olive" title="b4">n</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="flang_2.html#K1" title="FLANG_2:func.1">|^</a> (<font color="Olive" title="b3">m</font>,<font color="Olive" title="b4">n</font>)</span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Olive" title="b2">k</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">m</font>, <font color="Olive" title="b3">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="flang_2.html#K1" title="FLANG_2:func.1">|^</a> (<font color="Olive" title="b2">m</font>,<font color="Olive" title="b3">n</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_2.html#K1" title="FLANG_2:func.1">|^</a> (<font color="Olive" title="b2">m</font>,<font color="Olive" title="b3">n</font>)</span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Olive" title="b1">k</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">k</font>, <font color="Maroon" title="c4">m</font>, <font color="Maroon" title="c5">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="flang_2.html#K1" title="FLANG_2:func.1">|^</a> (<font color="Maroon" title="c4">m</font>,<font color="Maroon" title="c5">n</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_2.html#K1" title="FLANG_2:func.1">|^</a> (<font color="Maroon" title="c4">m</font>,<font color="Maroon" title="c5">n</font>)</span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">k</font></span><br/>









<a NAME="E1:44"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_2.html#K1" title="FLANG_2:func.1">|^</a> (<font color="Maroon" title="c4">m</font>,<font color="Maroon" title="c5">n</font>)</span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="flang_2.html#K1" title="FLANG_2:func.1">|^</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">k</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="flang_2.html#T40" target="_self" title="FLANG_2:th.40">Th40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:44"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="flang_2.html#K1" title="FLANG_2:func.1">|^</a> (<font color="Maroon" title="c4">m</font>,<font color="Maroon" title="c5">n</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_2.html#K1" title="FLANG_2:func.1">|^</a> (<font color="Maroon" title="c4">m</font>,<font color="Maroon" title="c5">n</font>)</span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="flang_2.html#T42" target="_self" title="FLANG_2:th.42">Th42</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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